Warped entanglement entropy

We study the applicability of the covariant holographic entanglement entropy proposal to asymptotically warped AdS3 spacetimes with an SL(2, ℝ) × U(1) isometry. We begin by applying the proposal to locally AdS3 backgrounds which are written as an ℝ1 fibration over AdS2. We then perturb away from this geometry by considering a warping parameter a = 1 + δ to get an asymptotically warped AdS3 spacetime and compute the dual entanglement entropy perturbatively in δ. We find that for large separation in the fiber coordinate, the entanglement entropy can be computed to all orders in δ and takes the universal form appropriate for two-dimensional CFTs. The warping-dependent central charge thus identified exactly agrees with previous calculations in the literature. Performing the same perturbative calculations for the warped BTZ black hole again gives universal two-dimensional CFT answers, with the left-moving and right-moving temperatures appearing appropriately in the result.